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151.
Wenguang Zhai 《中国科学A辑(英文版)》1999,42(11):1173-1183
Thek-dimensional Piatetski-Shapiro prime number problem fork⩾3 is studied. Let π(x
1
c
1,⋯,c
k
) denote the number of primesp withp⩽x,
, where 1<c
1<⋯<c
k
are fixed constants. It is proved that π(x;c
1,⋯,c
k
) has an asymptotic formula ifc
1
−1
+⋯+c
k
−1
>k−k/(4k
2+2).
Project supported by the National Natural Science Foundation of China (Grant No. 19801021) and the Natural Science Foundation
of Shandong Province (Grant No.Q98A02110). 相似文献
152.
Yasuhiro Gotoh 《Proceedings of the American Mathematical Society》1999,127(5):1443-1451
Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.
153.
A subset S of a d-dimensional convex body K is extensive if S
∂K and for any p, q ∈ S the distance between p and q is at least one-half of the maximum length of chords of K parallel to the segment pq. In this paper we establish the general upper bound |S| ≤ 3
d
— 1. We also find an upper bound for a certain class of 3-polytopes, which leads to the determination of the maximum cardinalities
of extensive subsets and their extremal configurations for tetrahedra, octahedra and some other 3-polytopes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
154.
Recently, differential geometric properties of embedded projective varieties have gained increasing interest. In this note, we consider plane algebraic curves equipped with the Fubini--Study metric from2 () and give an estimate for the diameter in terms of the degree, initiated in a paper by F. A. Bogomolov. 相似文献
155.
We show that the covering radius R of an [n,k,d] code over Fq is bounded above by R n-n
q(k, d/q). We strengthen this bound when R d and find conditions under which equality holds.As applications of this and other bounds, we show that all binary linear codes of lengths up to 15, or codimension up to 9, are normal. We also establish the normality of most codes of length 16 and many of codimension 10. These results have applications in the construction of codes that attain t[n,k,/it>], the smallest covering radius of any binary linear [n,k].We also prove some new results on the amalgamated direct sum (ADS) construction of Graham and Sloane. We find new conditions assuring normality of the ADS; covering radius 1 less than previously guaranteed for ADS of codes with even norms; good covering codes as ADS without the hypothesis of normality, from concepts p- stable and s- stable; codes with best known covering radii as ADS of two, often cyclic, codes (thus retaining structure so as to be suitable for practical applications). 相似文献
156.
Shigehiko Kuratsubo 《Proceedings of the American Mathematical Society》1999,127(10):2987-2994
We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.
157.
J. A. Cuesta-Albertos C. Matrán-Bea A. Tuero-Diaz 《Journal of Theoretical Probability》1996,9(2):263-283
We provide two families of lower bounds for theL
2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02. 相似文献
158.
Examples are given to show that the closest partition distance measure need not agree with the nearest neighbor interchange distance for unordered labeled binary trees. Proposed algorithms for computing the closest partition distance are shown to be of exponential complexity and hence may not be useful in approximating the nearest neighbor interchange distance. 相似文献
159.
160.